Off-campus UMass Amherst users: To download dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.
Non-UMass Amherst users, please click the view more button below to purchase a copy of this dissertation from Proquest.
(Some titles may also be available free of charge in our Open Access Dissertation Collection, so please check there first.)
Large deviation principles and complete equivalence and nonequivalence results for microcanonical and canonical ensembles with an application to geophysics
Abstract
We consider statistical mechanical models of a general class of physical systems for which large-scale, coherent structures persist amidst small-scale, turbulent fluctuations. The main focus of this dissertation is on whether a statistical mechanical formulation using a canonical ensemble yields equivalent predictions to a statistical mechanical formulation using a microcanonical ensemble. For each ensemble, a large deviation principle is proved, and the set of equilibrium macrostates is defined as the set on which the corresponding rate function attains its minimum of 0. A complete classification of all equivalence and nonequivalence relationships between the sets of canonical equilibrium macrostates and the sets of micro-canonical equilibrium macrostates are given in terms of concavity properties of the microcanonical entropy. The general theory of this dissertation is then applied to the specific, geophysical example of barotropic, quasi-geostrophic turbulence.
Subject Area
Mathematics|Geophysics|Statistics
Recommended Citation
Haven, Kyle Douglas, "Large deviation principles and complete equivalence and nonequivalence results for microcanonical and canonical ensembles with an application to geophysics" (2001). Doctoral Dissertations Available from Proquest. AAI3012136.
https://scholarworks.umass.edu/dissertations/AAI3012136